A Cosmological Constant That is Too Small

Abstract

We construct a vacuum of string theory in which the magnitude of the vacuum energy is < 10 −123 in Planck units. Regrettably, the sign of the vacuum energy is negative, and some supersymmetry remains unbroken.

On the Search for Low W0

“…The F-flatness condition is D 𝜏 W eff = (𝜕 𝜏 + 𝜕 𝜏 K)W eff = 0. Note that the form of the Kähler potential (22) implies that 𝜕 𝜏 K ∝ (Im𝜏) −1 = g s . Therefore, for consistent stabilisation at weak string coupling, the term involving 𝜕 𝜏 K must be a small correction to the F-flatness condition.…”

“…The paper [17] presented an explicit choice of flux quanta in an orientifold of the Calabi-Yau obtained by considering a degree-18 hypersurface in ℂℙ [1,1,1,6,9] , which yielded |W 0 | ∼ 10 −8 (for earlier work on obtaining low values of |W 0 | see for example [20,21] ). Not stopping at that, an explicit example with |W 0 | as low as 10 −95 was presented in [22,23]. Here, important advances were made in developing Kähler moduli stabilisation in this context.…”

On the Search for Low $W_0$

“…The paper [17] presented an explicit choice of flux quanta in an orientifold of the Calabi-Yau obtained by considering a degree-18 hypersurface in CP [1,1,1,6,9] , which yielded |W 0 | ∼ 10 −8 (for earlier work on obtaining low values of |W 0 | see for example [20,21]). Not stopping at that, an explicit example with |W 0 | as low as 10 −95 was presented in [22,23]. Here, important advances were made in developing Kähler moduli stabilisation in this context.…”

Analytic Periods via Twisted Symmetric Squares

“…The usual strategy when studying flux compactifications is to obtain locally valid expressions for these objects by expanding the periods of the CY around a point in moduli space and then requiring the fluxes to be chosen in a selfconsistent way such that the initially assumed approximation holds. As an example, the recently proposed constructions of exponentially small superpotentials [6][7][8][9][10][11][12][13] develop the periods around the large complex structure point (LCS) or the conifold and drop the higher order exponentially small corrections. Globally valid expressions for the periods remove this limitation and would allow easier scans over flux vacua.…”